def test_FinDateTenors(): startDate = FinDate(2018, 2, 23) tenor = "5d" print(tenor, startDate.addTenor(tenor)) tenor = "7D" print(tenor, startDate.addTenor(tenor)) tenor = "1W" print(tenor, startDate.addTenor(tenor)) tenor = "4W" print(tenor, startDate.addTenor(tenor)) tenor = "1M" print(tenor, startDate.addTenor(tenor)) tenor = "24M" print(tenor, startDate.addTenor(tenor)) tenor = "2Y" print(tenor, startDate.addTenor(tenor)) tenor = "10y" print(tenor, startDate.addTenor(tenor)) tenor = "0m" print(tenor, startDate.addTenor(tenor)) tenor = "20Y" print(tenor, startDate.addTenor(tenor))
def test_FinDateTenors(): startDate = FinDate(23, 2, 2018) testCases.header("TENOR", "DATE") tenor = "5d" testCases.print(tenor, startDate.addTenor(tenor)) tenor = "7D" testCases.print(tenor, startDate.addTenor(tenor)) tenor = "1W" testCases.print(tenor, startDate.addTenor(tenor)) tenor = "4W" testCases.print(tenor, startDate.addTenor(tenor)) tenor = "1M" testCases.print(tenor, startDate.addTenor(tenor)) tenor = "24M" testCases.print(tenor, startDate.addTenor(tenor)) tenor = "2Y" testCases.print(tenor, startDate.addTenor(tenor)) tenor = "10y" testCases.print(tenor, startDate.addTenor(tenor)) tenor = "0m" testCases.print(tenor, startDate.addTenor(tenor)) tenor = "20Y" testCases.print(tenor, startDate.addTenor(tenor))
def test_BlackKarasinskiExampleTwo(): # Valuation of a European option on a coupon bearing bond # This follows example in Fig 28.11 of John Hull's book but does not # have the exact same dt so there are some differences settlementDate = FinDate(1, 12, 2019) expiryDate = settlementDate.addTenor("18m") maturityDate = settlementDate.addTenor("10Y") coupon = 0.05 frequencyType = FinFrequencyTypes.SEMI_ANNUAL accrualType = FinDayCountTypes.ACT_ACT_ICMA bond = FinBond(maturityDate, coupon, frequencyType, accrualType) bond.calculateFlowDates(settlementDate) couponTimes = [] couponFlows = [] cpn = bond._coupon / bond._frequency for flowDate in bond._flowDates: flowTime = (flowDate - settlementDate) / gDaysInYear couponTimes.append(flowTime) couponFlows.append(cpn) couponTimes = np.array(couponTimes) couponFlows = np.array(couponFlows) strikePrice = 105.0 face = 100.0 tmat = (maturityDate - settlementDate) / gDaysInYear texp = (expiryDate - settlementDate) / gDaysInYear times = np.linspace(0, tmat, 20) dfs = np.exp(-0.05 * times) curve = FinDiscountCurve(settlementDate, times, dfs) price = bond.fullPriceFromDiscountCurve(settlementDate, curve) print("Fixed Income Price:", price) sigma = 0.20 a = 0.05 # Test convergence numStepsList = [100] #,101,200,300,400,500,600,700,800,900,1000] isAmerican = True treeVector = [] for numTimeSteps in numStepsList: start = time.time() model = FinModelRatesBlackKarasinski(a, sigma) model.buildTree(tmat, int(numTimeSteps), times, dfs) v = model.bondOption(texp, strikePrice, face, couponTimes, couponFlows, isAmerican) end = time.time() period = end - start treeVector.append(v[0]) print(numTimeSteps, v, period)
def test_HullWhiteExampleTwo(): # HULL BOOK ZERO COUPON BOND EXAMPLE 28.1 SEE TABLE 28.3 # Replication may not be exact as I am using dates rather than times zeroDays = [ 0, 3, 31, 62, 94, 185, 367, 731, 1096, 1461, 1826, 2194, 2558, 2922, 3287, 3653 ] zeroRates = [ 5.0, 5.01772, 4.98282, 4.97234, 4.96157, 4.99058, 5.09389, 5.79733, 6.30595, 6.73464, 6.94816, 7.08807, 7.27527, 7.30852, 7.39790, 7.49015 ] times = np.array(zeroDays) / 365.0 zeros = np.array(zeroRates) / 100.0 dfs = np.exp(-zeros * times) startDate = FinDate(1, 12, 2019) sigma = 0.01 a = 0.1 strike = 63.0 face = 100.0 expiryDate = startDate.addTenor("3Y") maturityDate = startDate.addTenor("9Y") texp = (expiryDate - startDate) / gDaysInYear tmat = (maturityDate - startDate) / gDaysInYear model = FinHullWhiteRateModel(a, sigma) vAnal = model.optionOnZeroCouponBond(texp, tmat, strike, face, times, dfs) # Test convergence numStepsList = range(100, 500, 10) analVector = [] treeVector = [] for numTimeSteps in numStepsList: start = time.time() model.buildTree(texp, numTimeSteps, times, dfs) vTree = model.optionOnZeroCouponBond_Tree(texp, tmat, strike, face) end = time.time() period = end - start treeVector.append(vTree[1]) analVector.append(vAnal[1]) print(numTimeSteps, vTree, vAnal, period) plt.plot(numStepsList, treeVector) plt.plot(numStepsList, analVector)
def test_FinBondMortgage(): principal = 130000 startDate = FinDate(23, 2, 2018) endDate = startDate.addTenor("10Y") mortgage = FinBondMortgage(startDate, endDate, principal) rate = 0.035 mortgage.generateFlows(rate, FinBondMortgageTypes.REPAYMENT) numFlows = len(mortgage._schedule._adjustedDates) testCases.header("PAYMENT DATE", "INTEREST", "PRINCIPAL", "OUTSTANDING", "TOTAL") for i in range(0, numFlows): testCases.print(mortgage._schedule._adjustedDates[i], mortgage._interestFlows[i], mortgage._principalFlows[i], mortgage._principalRemaining[i], mortgage._totalFlows[i]) mortgage.generateFlows(rate, FinBondMortgageTypes.INTEREST_ONLY) testCases.header("PAYMENT DATE", "INTEREST", "PRINCIPAL", "OUTSTANDING", "TOTAL") for i in range(0, numFlows): testCases.print(mortgage._schedule._adjustedDates[i], mortgage._interestFlows[i], mortgage._principalFlows[i], mortgage._principalRemaining[i], mortgage._totalFlows[i])
def test_FinScheduleAlignmentEff31(): ''' EOM schedule so all unadjusted dates fall on month end.''' eomFlag = True valuationDate = FinDate(29, 7, 2006) effDate = valuationDate.addTenor("2D") freqType = FinFrequencyTypes.SEMI_ANNUAL busDayAdjustType = FinBusDayAdjustTypes.MODIFIED_FOLLOWING dateGenRuleType = FinDateGenRuleTypes.BACKWARD calendarType = FinCalendarTypes.UNITED_STATES adjustTerminationDate = True matDate1 = effDate.addTenor("4Y") matDate2 = effDate.addTenor("50Y") # print(matDate1, matDate2) sched1 = FinSchedule(effDate, matDate1, freqType, calendarType, busDayAdjustType, dateGenRuleType, adjustTerminationDate, eomFlag) sched2 = FinSchedule(effDate, matDate2, freqType, calendarType, busDayAdjustType, dateGenRuleType, adjustTerminationDate, eomFlag) # print(sched1._adjustedDates) # print(sched2._adjustedDates[:len(sched1._adjustedDates)]) compare = (sched1._adjustedDates[-1] == sched2._adjustedDates[ len(sched1._adjustedDates) - 1]) assert (compare == True)
def test_FinScheduleAlignmentLeapYearNotEOM(): ''' Effective date on leap year. Not EOM. ''' eomFlag = False valuationDate = FinDate(26, 2, 2006) effDate = valuationDate.addTenor("2D") freqType = FinFrequencyTypes.SEMI_ANNUAL busDayAdjustType = FinBusDayAdjustTypes.MODIFIED_FOLLOWING dateGenRuleType = FinDateGenRuleTypes.BACKWARD calendarType = FinCalendarTypes.UNITED_STATES adjustTerminationDate = True matDate1 = effDate.addTenor("4Y") matDate2 = effDate.addTenor("50Y") # print(matDate1, matDate2) sched1 = FinSchedule(effDate, matDate1, freqType, calendarType, busDayAdjustType, dateGenRuleType, adjustTerminationDate, eomFlag) sched2 = FinSchedule(effDate, matDate2, freqType, calendarType, busDayAdjustType, dateGenRuleType, adjustTerminationDate, eomFlag) # print(sched1._adjustedDates) # print(sched2._adjustedDates[:len(sched1._adjustedDates)]) compare = (sched1._adjustedDates[-1] == sched2._adjustedDates[ len(sched1._adjustedDates) - 1]) assert (compare == True)
def test_FinBondOption(): settlementDate = FinDate(1, 12, 2019) maturityDate = settlementDate.addTenor("10Y") coupon = 0.05 frequencyType = FinFrequencyTypes.SEMI_ANNUAL accrualType = FinDayCountTypes.ACT_ACT_ICMA bond = FinBond(maturityDate, coupon, frequencyType, accrualType) tmat = (maturityDate - settlementDate) / gDaysInYear times = np.linspace(0, tmat, 20) dfs = np.exp(-0.05 * times) discountCurve = FinDiscountCurve(settlementDate, times, dfs) expiryDate = settlementDate.addTenor("18m") strikePrice = 105.0 face = 100.0 optionType = FinBondOptionTypes.AMERICAN_CALL price = bond.fullPriceFromDiscountCurve(settlementDate, discountCurve) print("Fixed Income Price:", price) for strikePrice in [90, 95, 100, 105, 110]: sigma = 0.01 a = 0.1 bondOption = FinBondOption(bond, expiryDate, strikePrice, face, optionType) model = FinModelRatesHullWhite(a, sigma) v = bondOption.value(settlementDate, discountCurve, model) print("HW", strikePrice, v) for strikePrice in [90, 95, 100, 105, 110]: sigma = 0.20 a = 0.05 bondOption = FinBondOption(bond, expiryDate, strikePrice, face, optionType) model = FinModelRatesBlackKarasinski(a, sigma) v = bondOption.value(settlementDate, discountCurve, model) print("BK", strikePrice, v)
def test_FinBondMortgage(): principal = 130000 startDate = FinDate(23, 2, 2018) endDate = startDate.addTenor("10Y") mortgage = FinBondMortgage(startDate, endDate, principal) rate = 0.035 mortgage.generateFlows(rate, FinBondMortgageType.REPAYMENT) mortgage.print() mortgage.generateFlows(rate, FinBondMortgageType.INTEREST_ONLY) mortgage.print()
def test_FinScheduleAlignment(eomFlag): valuationDate = FinDate(29, 3, 2005) effDate = valuationDate.addTenor("2d") freqType = FinFrequencyTypes.SEMI_ANNUAL busDayAdjustType = FinBusDayAdjustTypes.MODIFIED_FOLLOWING dateGenRuleType = FinDateGenRuleTypes.BACKWARD calendarType = FinCalendarTypes.UNITED_STATES adjustTerminationDate = False matDate1 = effDate.addTenor("4Y") matDate2 = effDate.addTenor("50Y") # print(matDate1) # print(matDate2) myCal = FinCalendar(calendarType) adjustedMatDate1 = myCal.adjust(matDate1, busDayAdjustType) adjustedMatDate2 = myCal.adjust(matDate2, busDayAdjustType) # print(adjustedMatDate1) # print(adjustedMatDate2) sched1 = FinSchedule(effDate, adjustedMatDate1, freqType, calendarType, busDayAdjustType, dateGenRuleType, adjustTerminationDate, eomFlag) # print(sched1) sched2 = FinSchedule(effDate, adjustedMatDate2, freqType, calendarType, busDayAdjustType, dateGenRuleType, adjustTerminationDate, eomFlag) compare = (sched1._adjustedDates[-1] == sched2._adjustedDates[len(sched1._adjustedDates)-1]) assert(compare == eomFlag)
def test_HullWhiteCallableBond(): # Valuation of a European option on a coupon bearing bond settlementDate = FinDate(1, 12, 2019) issueDate = FinDate(1, 12, 2018) maturityDate = settlementDate.addTenor("10Y") coupon = 0.05 frequencyType = FinFrequencyTypes.SEMI_ANNUAL accrualType = FinDayCountTypes.ACT_ACT_ICMA bond = FinBond(issueDate, maturityDate, coupon, frequencyType, accrualType) couponTimes = [] couponFlows = [] cpn = bond._coupon / bond._frequency for flowDate in bond._flowDates[1:]: if flowDate > settlementDate: flowTime = (flowDate - settlementDate) / gDaysInYear couponTimes.append(flowTime) couponFlows.append(cpn) couponTimes = np.array(couponTimes) couponFlows = np.array(couponFlows) ########################################################################### # Set up the call and put times and prices ########################################################################### callDates = [] callPrices = [] callPx = 120.0 callDates.append(settlementDate.addTenor("2Y")) callPrices.append(callPx) callDates.append(settlementDate.addTenor("3Y")) callPrices.append(callPx) callDates.append(settlementDate.addTenor("4Y")) callPrices.append(callPx) callDates.append(settlementDate.addTenor("5Y")) callPrices.append(callPx) callDates.append(settlementDate.addTenor("6Y")) callPrices.append(callPx) callDates.append(settlementDate.addTenor("7Y")) callPrices.append(callPx) callDates.append(settlementDate.addTenor("8Y")) callPrices.append(callPx) callTimes = [] for dt in callDates: t = (dt - settlementDate) / gDaysInYear callTimes.append(t) putDates = [] putPrices = [] putPx = 98.0 putDates.append(settlementDate.addTenor("2Y")) putPrices.append(putPx) putDates.append(settlementDate.addTenor("3Y")) putPrices.append(putPx) putDates.append(settlementDate.addTenor("4Y")) putPrices.append(putPx) putDates.append(settlementDate.addTenor("5Y")) putPrices.append(putPx) putDates.append(settlementDate.addTenor("6Y")) putPrices.append(putPx) putDates.append(settlementDate.addTenor("7Y")) putPrices.append(putPx) putDates.append(settlementDate.addTenor("8Y")) putPrices.append(putPx) putTimes = [] for dt in putDates: t = (dt - settlementDate) / gDaysInYear putTimes.append(t) ########################################################################### tmat = (maturityDate - settlementDate) / gDaysInYear curve = FinDiscountCurveFlat(settlementDate, 0.05, FinFrequencyTypes.CONTINUOUS) dfs = [] times = [] for dt in bond._flowDates: if dt > settlementDate: t = (dt - settlementDate) / gDaysInYear df = curve.df(dt) times.append(t) dfs.append(df) dfs = np.array(dfs) times = np.array(times) ########################################################################### v1 = bond.cleanPriceFromDiscountCurve(settlementDate, curve) sigma = 0.02 # basis point volatility a = 0.01 # Test convergence numStepsList = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000] tmat = (maturityDate - settlementDate) / gDaysInYear testCases.header("NUMSTEPS", "BOND_ONLY", "CALLABLE_BOND", "TIME") for numTimeSteps in numStepsList: start = time.time() model = FinModelRatesHW(sigma, a, numTimeSteps) model.buildTree(tmat, times, dfs) v2 = model.callablePuttableBond_Tree(couponTimes, couponFlows, callTimes, callPrices, putTimes, putPrices, 100.0) end = time.time() period = end - start testCases.print(numTimeSteps, v1, v2, period)
def test_HullWhiteCallableBond(): # Valuation of a European option on a coupon bearing bond settlementDate = FinDate(1, 12, 2019) maturityDate = settlementDate.addTenor("10Y") coupon = 0.05 frequencyType = FinFrequencyTypes.SEMI_ANNUAL accrualType = FinDayCountTypes.ACT_ACT_ICMA bond = FinBond(maturityDate, coupon, frequencyType, accrualType) bond.calculateFlowDates(settlementDate) couponTimes = [] couponFlows = [] cpn = bond._coupon / bond._frequency for flowDate in bond._flowDates[1:]: flowTime = (flowDate - settlementDate) / gDaysInYear couponTimes.append(flowTime) couponFlows.append(cpn) couponTimes = np.array(couponTimes) couponFlows = np.array(couponFlows) ########################################################################### # Set up the call and put times and prices ########################################################################### callDates = [] callPrices = [] callPx = 120.0 callDates.append(settlementDate.addTenor("5Y")) callPrices.append(callPx) callDates.append(settlementDate.addTenor("6Y")) callPrices.append(callPx) callDates.append(settlementDate.addTenor("7Y")) callPrices.append(callPx) callDates.append(settlementDate.addTenor("8Y")) callPrices.append(callPx) callTimes = [] for dt in callDates: t = (dt - settlementDate) / gDaysInYear callTimes.append(t) putDates = [] putPrices = [] putPx = 98.0 putDates.append(settlementDate.addTenor("5Y")) putPrices.append(putPx) putDates.append(settlementDate.addTenor("6Y")) putPrices.append(putPx) putDates.append(settlementDate.addTenor("7Y")) putPrices.append(putPx) putDates.append(settlementDate.addTenor("8Y")) putPrices.append(putPx) putTimes = [] for dt in putDates: t = (dt - settlementDate) / gDaysInYear putTimes.append(t) ########################################################################### tmat = (maturityDate - settlementDate) / gDaysInYear times = np.linspace(0, tmat, 20) dfs = np.exp(-0.05 * times) curve = FinDiscountCurve(settlementDate, times, dfs) ########################################################################### v1 = bond.fullPriceFromDiscountCurve(settlementDate, curve) sigma = 0.02 # basis point volatility a = 0.1 # Test convergence numStepsList = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000] tmat = (maturityDate - settlementDate) / gDaysInYear print("NUMSTEPS", "BOND_ONLY", "CALLABLE_BOND", "TIME") for numTimeSteps in numStepsList: start = time.time() model = FinModelRatesHullWhite(a, sigma) model.buildTree(tmat, numTimeSteps, times, dfs) v2 = model.callablePuttableBond_Tree(couponTimes, couponFlows, callTimes, callPrices, putTimes, putPrices) end = time.time() period = end - start print(numTimeSteps, v1, v2, period) if 1 == 0: print("RT") printTree(model._rt, 5) print("BOND") printTree(model._bondValues, 5) print("OPTION") printTree(model._optionValues, 5)
def testFinLiborCashSettledSwaption(): testCases.header("LABEL", "VALUE") valuationDate = FinDate(1, 1, 2020) settlementDate = FinDate(1, 1, 2020) depoDCCType = FinDayCountTypes.THIRTY_E_360_ISDA depos = [] depo = FinLiborDeposit(settlementDate, "1W", 0.0023, depoDCCType) depos.append(depo) depo = FinLiborDeposit(settlementDate, "1M", 0.0023, depoDCCType) depos.append(depo) depo = FinLiborDeposit(settlementDate, "3M", 0.0023, depoDCCType) depos.append(depo) depo = FinLiborDeposit(settlementDate, "6M", 0.0023, depoDCCType) depos.append(depo) # No convexity correction provided so I omit interest rate futures settlementDate = FinDate(2, 1, 2020) swaps = [] accType = FinDayCountTypes.ACT_365F fixedFreqType = FinFrequencyTypes.SEMI_ANNUAL swapType = FinLiborSwapTypes.PAYER swap = FinLiborSwap(settlementDate, "3Y", swapType, 0.00790, fixedFreqType, accType) swaps.append(swap) swap = FinLiborSwap(settlementDate, "4Y", swapType, 0.01200, fixedFreqType, accType) swaps.append(swap) swap = FinLiborSwap(settlementDate, "5Y", swapType, 0.01570, fixedFreqType, accType) swaps.append(swap) swap = FinLiborSwap(settlementDate, "6Y", swapType, 0.01865, fixedFreqType, accType) swaps.append(swap) swap = FinLiborSwap(settlementDate, "7Y", swapType, 0.02160, fixedFreqType, accType) swaps.append(swap) swap = FinLiborSwap(settlementDate, "8Y", swapType, 0.02350, fixedFreqType, accType) swaps.append(swap) swap = FinLiborSwap(settlementDate, "9Y", swapType, 0.02540, fixedFreqType, accType) swaps.append(swap) swap = FinLiborSwap(settlementDate, "10Y", swapType, 0.0273, fixedFreqType, accType) swaps.append(swap) swap = FinLiborSwap(settlementDate, "15Y", swapType, 0.0297, fixedFreqType, accType) swaps.append(swap) swap = FinLiborSwap(settlementDate, "20Y", swapType, 0.0316, fixedFreqType, accType) swaps.append(swap) swap = FinLiborSwap(settlementDate, "25Y", swapType, 0.0335, fixedFreqType, accType) swaps.append(swap) swap = FinLiborSwap(settlementDate, "30Y", swapType, 0.0354, fixedFreqType, accType) swaps.append(swap) liborCurve = FinLiborCurve(valuationDate, depos, [], swaps, FinInterpTypes.LINEAR_ZERO_RATES) exerciseDate = settlementDate.addTenor("5Y") swapMaturityDate = exerciseDate.addTenor("5Y") swapFixedCoupon = 0.040852 swapFixedFrequencyType = FinFrequencyTypes.SEMI_ANNUAL swapFixedDayCountType = FinDayCountTypes.THIRTY_E_360_ISDA swapFloatFrequencyType = FinFrequencyTypes.QUARTERLY swapFloatDayCountType = FinDayCountTypes.ACT_360 swapNotional = 1000000 swaptionType = FinLiborSwapTypes.PAYER swaption = FinLiborSwaption(settlementDate, exerciseDate, swapMaturityDate, swaptionType, swapFixedCoupon, swapFixedFrequencyType, swapFixedDayCountType, swapNotional, swapFloatFrequencyType, swapFloatDayCountType) model = FinModelBlack(0.1533) v = swaption.value(settlementDate, liborCurve, model) testCases.print("Swaption No-Arb Value:", v) fwdSwapRate = liborCurve.swapRate(valuationDate, swapMaturityDate, swapFixedFrequencyType, swapFixedDayCountType) testCases.print("Fwd Swap Rate:", fwdSwapRate) model = FinModelBlack(0.1533) v = swaption.cashSettledValue(valuationDate, liborCurve, fwdSwapRate, model) testCases.print("Swaption Cash Settled Value:", v)
def test_FinLiborSwaptionQLExample(): # valuationDate = FinDate(28, 2, 2014) settlementDate = FinDate(4, 3, 2014) depoDCCType = FinDayCountTypes.THIRTY_E_360_ISDA depos = [] depo = FinLiborDeposit(settlementDate, "1W", 0.0023, depoDCCType) depos.append(depo) depo = FinLiborDeposit(settlementDate, "1M", 0.0023, depoDCCType) depos.append(depo) depo = FinLiborDeposit(settlementDate, "3M", 0.0023, depoDCCType) depos.append(depo) depo = FinLiborDeposit(settlementDate, "6M", 0.0023, depoDCCType) depos.append(depo) # No convexity correction provided so I omit interest rate futures swaps = [] accType = FinDayCountTypes.ACT_365F fixedFreqType = FinFrequencyTypes.SEMI_ANNUAL swapType = FinLiborSwapTypes.PAYER swap = FinLiborSwap(settlementDate, "3Y", swapType, 0.00790, fixedFreqType, accType) swaps.append(swap) swap = FinLiborSwap(settlementDate, "4Y", swapType, 0.01200, fixedFreqType, accType) swaps.append(swap) swap = FinLiborSwap(settlementDate, "5Y", swapType, 0.01570, fixedFreqType, accType) swaps.append(swap) swap = FinLiborSwap(settlementDate, "6Y", swapType, 0.01865, fixedFreqType, accType) swaps.append(swap) swap = FinLiborSwap(settlementDate, "7Y", swapType, 0.02160, fixedFreqType, accType) swaps.append(swap) swap = FinLiborSwap(settlementDate, "8Y", swapType, 0.02350, fixedFreqType, accType) swaps.append(swap) swap = FinLiborSwap(settlementDate, "9Y", swapType, 0.02540, fixedFreqType, accType) swaps.append(swap) swap = FinLiborSwap(settlementDate, "10Y", swapType, 0.0273, fixedFreqType, accType) swaps.append(swap) swap = FinLiborSwap(settlementDate, "15Y", swapType, 0.0297, fixedFreqType, accType) swaps.append(swap) swap = FinLiborSwap(settlementDate, "20Y", swapType, 0.0316, fixedFreqType, accType) swaps.append(swap) swap = FinLiborSwap(settlementDate, "25Y", swapType, 0.0335, fixedFreqType, accType) swaps.append(swap) swap = FinLiborSwap(settlementDate, "30Y", swapType, 0.0354, fixedFreqType, accType) swaps.append(swap) liborCurve = FinLiborCurve(settlementDate, depos, [], swaps, FinInterpTypes.LINEAR_ZERO_RATES) exerciseDate = settlementDate.addTenor("5Y") swapMaturityDate = exerciseDate.addTenor("5Y") swapFixedCoupon = 0.040852 swapFixedFrequencyType = FinFrequencyTypes.SEMI_ANNUAL swapFixedDayCountType = FinDayCountTypes.THIRTY_E_360_ISDA swapFloatFrequencyType = FinFrequencyTypes.QUARTERLY swapFloatDayCountType = FinDayCountTypes.ACT_360 swapNotional = 1000000 swaptionType = FinLiborSwapTypes.PAYER swaption = FinLiborSwaption(settlementDate, exerciseDate, swapMaturityDate, swaptionType, swapFixedCoupon, swapFixedFrequencyType, swapFixedDayCountType, swapNotional, swapFloatFrequencyType, swapFloatDayCountType) testCases.header("MODEL", "VALUE") model = FinModelBlack(0.1533) v = swaption.value(settlementDate, liborCurve, model) testCases.print(model.__class__, v) model = FinModelBlackShifted(0.1533, -0.008) v = swaption.value(settlementDate, liborCurve, model) testCases.print(model.__class__, v) model = FinModelSABR(0.132, 0.5, 0.5, 0.5) v = swaption.value(settlementDate, liborCurve, model) testCases.print(model.__class__, v) model = FinModelSABRShifted(0.352, 0.5, 0.15, 0.15, -0.005) v = swaption.value(settlementDate, liborCurve, model) testCases.print(model.__class__, v) model = FinModelRatesHW(0.010000000, 0.00000000001) v = swaption.value(settlementDate, liborCurve, model) testCases.print(model.__class__, v)
def test_HullWhiteBondOption(): # Valuation of a European option on a coupon bearing bond settlementDate = FinDate(1, 12, 2019) expiryDate = settlementDate.addTenor("18m") maturityDate = settlementDate.addTenor("10Y") coupon = 0.05 frequencyType = FinFrequencyTypes.SEMI_ANNUAL accrualType = FinDayCountTypes.ACT_ACT_ICMA bond = FinBond(maturityDate, coupon, frequencyType, accrualType) bond.calculateFlowDates(settlementDate) couponTimes = [] couponFlows = [] cpn = bond._coupon / bond._frequency for flowDate in bond._flowDates[1:]: flowTime = (flowDate - settlementDate) / gDaysInYear couponTimes.append(flowTime) couponFlows.append(cpn) couponTimes = np.array(couponTimes) couponFlows = np.array(couponFlows) strikePrice = 105.0 face = 100.0 tmat = (maturityDate - settlementDate) / gDaysInYear times = np.linspace(0, tmat, 20) dfs = np.exp(-0.05 * times) curve = FinDiscountCurve(settlementDate, times, dfs) price = bond.fullPriceFromDiscountCurve(settlementDate, curve) print("Spot Bond Price:", price) price = bond.fullPriceFromDiscountCurve(expiryDate, curve) print("Fwd Bond Price:", price) sigma = 0.01 a = 0.1 # Test convergence numStepsList = [100, 200, 300, 400, 500] texp = (expiryDate - settlementDate) / gDaysInYear print("NUMSTEPS", "FAST TREE", "FULLTREE", "TIME") for numTimeSteps in numStepsList: start = time.time() model = FinModelRatesHullWhite(a, sigma) model.buildTree(texp, numTimeSteps, times, dfs) americanExercise = False v1 = model.americanBondOption_Tree(texp, strikePrice, face, couponTimes, couponFlows, americanExercise) v2 = model.europeanBondOption_Tree(texp, strikePrice, face, couponTimes, couponFlows) end = time.time() period = end - start print(numTimeSteps, v1, v2, period) # plt.plot(numStepsList, treeVector) if 1 == 0: print("RT") printTree(model._rt, 5) print("BOND") printTree(model._bondValues, 5) print("OPTION") printTree(model._optionValues, 5) v = model.europeanBondOption_Jamshidian(texp, strikePrice, face, couponTimes, couponFlows, times, dfs) print("EUROPEAN BOND JAMSHIDIAN DECOMP", v)
def test_FinBondOption(): settlementDate = FinDate(1, 12, 2019) issueDate = FinDate(1, 12, 2018) maturityDate = settlementDate.addTenor("10Y") coupon = 0.05 freqType = FinFrequencyTypes.SEMI_ANNUAL accrualType = FinDayCountTypes.ACT_ACT_ICMA bond = FinBond(issueDate, maturityDate, coupon, freqType, accrualType) times = np.linspace(0, 10.0, 21) dfs = np.exp(-0.05 * times) dates = settlementDate.addYears(times) discountCurve = FinDiscountCurve(settlementDate, dates, dfs) expiryDate = settlementDate.addTenor("18m") strikePrice = 105.0 face = 100.0 ########################################################################### strikes = [80, 85, 90, 95, 100, 105, 110, 115, 120] optionType = FinOptionTypes.EUROPEAN_CALL testCases.header("LABEL", "VALUE") price = bond.cleanPriceFromDiscountCurve(settlementDate, discountCurve) testCases.print("Fixed Income Price:", price) numTimeSteps = 100 testCases.banner("HW EUROPEAN CALL") testCases.header("STRIKE", "VALUE") for strikePrice in strikes: sigma = 0.01 a = 0.1 bondOption = FinBondOption(bond, expiryDate, strikePrice, face, optionType) model = FinModelRatesHW(sigma, a, numTimeSteps) v = bondOption.value(settlementDate, discountCurve, model) testCases.print(strikePrice, v) ########################################################################### optionType = FinOptionTypes.AMERICAN_CALL price = bond.cleanPriceFromDiscountCurve(settlementDate, discountCurve) testCases.header("LABEL", "VALUE") testCases.print("Fixed Income Price:", price) testCases.banner("HW AMERICAN CALL") testCases.header("STRIKE", "VALUE") for strikePrice in strikes: sigma = 0.01 a = 0.1 bondOption = FinBondOption(bond, expiryDate, strikePrice, face, optionType) model = FinModelRatesHW(sigma, a) v = bondOption.value(settlementDate, discountCurve, model) testCases.print(strikePrice, v) ########################################################################### optionType = FinOptionTypes.EUROPEAN_PUT testCases.banner("HW EUROPEAN PUT") testCases.header("STRIKE", "VALUE") price = bond.cleanPriceFromDiscountCurve(settlementDate, discountCurve) for strikePrice in strikes: sigma = 0.01 a = 0.1 bondOption = FinBondOption(bond, expiryDate, strikePrice, face, optionType) model = FinModelRatesHW(sigma, a) v = bondOption.value(settlementDate, discountCurve, model) testCases.print(strikePrice, v) ########################################################################### optionType = FinOptionTypes.AMERICAN_PUT testCases.banner("HW AMERICAN PUT") testCases.header("STRIKE", "VALUE") price = bond.cleanPriceFromDiscountCurve(settlementDate, discountCurve) for strikePrice in strikes: sigma = 0.02 a = 0.1 bondOption = FinBondOption(bond, expiryDate, strikePrice, face, optionType) model = FinModelRatesHW(sigma, a) v = bondOption.value(settlementDate, discountCurve, model) testCases.print(strikePrice, v)
def test_FinBondOptionZEROVOLConvergence(): # Build discount curve settlementDate = FinDate(1, 12, 2019) # CHANGED rate = 0.05 discountCurve = FinDiscountCurveFlat(settlementDate, rate, FinFrequencyTypes.ANNUAL) # Bond details issueDate = FinDate(1, 9, 2015) maturityDate = FinDate(1, 9, 2025) coupon = 0.06 freqType = FinFrequencyTypes.ANNUAL accrualType = FinDayCountTypes.ACT_ACT_ICMA bond = FinBond(issueDate, maturityDate, coupon, freqType, accrualType) # Option Details expiryDate = settlementDate.addTenor("18m") # FinDate(1, 12, 2021) # print("EXPIRY:", expiryDate) face = 100.0 dfExpiry = discountCurve.df(expiryDate) spotCleanValue = bond.cleanPriceFromDiscountCurve(settlementDate, discountCurve) fwdCleanValue = bond.cleanPriceFromDiscountCurve(expiryDate, discountCurve) # print("BOND SpotCleanBondPx", spotCleanValue) # print("BOND FwdCleanBondPx", fwdCleanValue) # print("BOND Accrued:", bond._accruedInterest) spotCleanValue = bond.cleanPriceFromDiscountCurve(settlementDate, discountCurve) testCases.header("STRIKE", "STEPS", "CALL_INT", "CALL_INT_PV", "CALL_EUR", "CALL_AMER", "PUT_INT", "PUT_INT_PV", "PUT_EUR", "PUT_AMER") numTimeSteps = range(100, 1000, 200) strikePrices = [90, 100, 110, 120] for strikePrice in strikePrices: callIntrinsic = max(spotCleanValue - strikePrice, 0) putIntrinsic = max(strikePrice - spotCleanValue, 0) callIntrinsicPV = max(fwdCleanValue - strikePrice, 0) * dfExpiry putIntrinsicPV = max(strikePrice - fwdCleanValue, 0) * dfExpiry for numSteps in numTimeSteps: sigma = 0.0000001 model = FinModelRatesBDT(sigma, numSteps) optionType = FinOptionTypes.EUROPEAN_CALL bondOption1 = FinBondOption(bond, expiryDate, strikePrice, face, optionType) v1 = bondOption1.value(settlementDate, discountCurve, model) optionType = FinOptionTypes.AMERICAN_CALL bondOption2 = FinBondOption(bond, expiryDate, strikePrice, face, optionType) v2 = bondOption2.value(settlementDate, discountCurve, model) optionType = FinOptionTypes.EUROPEAN_PUT bondOption3 = FinBondOption(bond, expiryDate, strikePrice, face, optionType) v3 = bondOption3.value(settlementDate, discountCurve, model) optionType = FinOptionTypes.AMERICAN_PUT bondOption4 = FinBondOption(bond, expiryDate, strikePrice, face, optionType) v4 = bondOption4.value(settlementDate, discountCurve, model) testCases.print(strikePrice, numSteps, callIntrinsic, callIntrinsicPV, v1, v2, putIntrinsic, putIntrinsicPV, v3, v4)
def test_FinBondOptionAmericanConvergenceTWO(): # Build discount curve settlementDate = FinDate(1, 12, 2019) discountCurve = FinDiscountCurveFlat(settlementDate, 0.05, FinFrequencyTypes.CONTINUOUS) # Bond details issueDate = FinDate(1, 9, 2014) maturityDate = FinDate(1, 9, 2025) coupon = 0.05 freqType = FinFrequencyTypes.ANNUAL accrualType = FinDayCountTypes.ACT_ACT_ICMA bond = FinBond(issueDate, maturityDate, coupon, freqType, accrualType) expiryDate = settlementDate.addTenor("18m") face = 100.0 spotValue = bond.fullPriceFromDiscountCurve(settlementDate, discountCurve) testCases.header("LABEL", "VALUE") testCases.print("BOND PRICE", spotValue) testCases.header("TIME", "N", "EUR_CALL", "AMER_CALL", "EUR_PUT", "AMER_PUT") sigma = 0.2 model = FinModelRatesBDT(sigma) K = 101.0 vec_ec = [] vec_ac = [] vec_ep = [] vec_ap = [] if 1 == 1: K = 100.0 bkModel = FinModelRatesBDT(sigma, 100) europeanCallBondOption = FinBondOption(bond, expiryDate, K, face, FinOptionTypes.EUROPEAN_CALL) v_ec = europeanCallBondOption.value(settlementDate, discountCurve, model) testCases.header("LABEL", "VALUE") testCases.print("OPTION", v_ec) numStepsVector = range(100, 100, 1) # should be 100-400 for numSteps in numStepsVector: bkModel = FinModelRatesBDT(sigma, numSteps) start = time.time() europeanCallBondOption = FinBondOption(bond, expiryDate, K, face, FinOptionTypes.EUROPEAN_CALL) v_ec = europeanCallBondOption.value(settlementDate, discountCurve, bkModel) americanCallBondOption = FinBondOption(bond, expiryDate, K, face, FinOptionTypes.AMERICAN_CALL) v_ac = americanCallBondOption.value(settlementDate, discountCurve, bkModel) europeanPutBondOption = FinBondOption(bond, expiryDate, K, face, FinOptionTypes.EUROPEAN_PUT) v_ep = europeanPutBondOption.value(settlementDate, discountCurve, bkModel) americanPutBondOption = FinBondOption(bond, expiryDate, K, face, FinOptionTypes.AMERICAN_PUT) v_ap = americanPutBondOption.value(settlementDate, discountCurve, bkModel) end = time.time() period = end - start testCases.print(period, numSteps, v_ec, v_ac, v_ep, v_ap) vec_ec.append(v_ec) vec_ac.append(v_ac) vec_ep.append(v_ep) vec_ap.append(v_ap) if plotGraphs: plt.figure() plt.plot(numStepsVector, vec_ec, label="European Call") plt.legend() plt.figure() plt.plot(numStepsVector, vec_ac, label="American Call") plt.legend() plt.figure() plt.plot(numStepsVector, vec_ep, label="European Put") plt.legend() plt.figure() plt.plot(numStepsVector, vec_ap, label="American Put") plt.legend()
def test_HullWhiteBondOption(): # Valuation of a European option on a coupon bearing bond settlementDate = FinDate(1, 12, 2019) issueDate = FinDate(1, 12, 2018) expiryDate = settlementDate.addTenor("18m") maturityDate = settlementDate.addTenor("10Y") coupon = 0.05 frequencyType = FinFrequencyTypes.SEMI_ANNUAL accrualType = FinDayCountTypes.ACT_ACT_ICMA bond = FinBond(issueDate, maturityDate, coupon, frequencyType, accrualType) couponTimes = [] couponFlows = [] cpn = bond._coupon / bond._frequency numFlows = len(bond._flowDates) for i in range(1, numFlows): pcd = bond._flowDates[i - 1] ncd = bond._flowDates[i] if ncd > settlementDate: if len(couponTimes) == 0: flowTime = (pcd - settlementDate) / gDaysInYear couponTimes.append(flowTime) couponFlows.append(cpn) flowTime = (ncd - settlementDate) / gDaysInYear couponTimes.append(flowTime) couponFlows.append(cpn) couponTimes = np.array(couponTimes) couponFlows = np.array(couponFlows) strikePrice = 100.0 face = 100.0 y = 0.05 times = np.linspace(0, 10, 21) dfs = np.power(1 + y / 2, -times * 2) sigma = 0.0000001 a = 0.1 model = FinModelRatesHW(sigma, a, None) # Test convergence numStepsList = range(20, 500, 10) texp = (expiryDate - settlementDate) / gDaysInYear vJam = model.europeanBondOptionJamshidian(texp, strikePrice, face, couponTimes, couponFlows, times, dfs) testCases.banner( "Pricing bond option on tree that goes to bond maturity and one using european bond option tree that goes to expiry." ) testCases.header("NUMSTEPS", "EXPIRY_ONLY", "EXPIRY_TREE", "JAMSHIDIAN", "TIME") for numTimeSteps in numStepsList: start = time.time() model = FinModelRatesHW(sigma, a, numTimeSteps, FinHWEuropeanCalcType.EXPIRY_ONLY) model.buildTree(texp, times, dfs) exerciseType = FinOptionExerciseTypes.EUROPEAN v1 = model.bondOption(texp, strikePrice, face, couponTimes, couponFlows, exerciseType) model = FinModelRatesHW(sigma, a, numTimeSteps, FinHWEuropeanCalcType.EXPIRY_TREE) model.buildTree(texp, times, dfs) v2 = model.bondOption(texp, strikePrice, face, couponTimes, couponFlows, exerciseType) end = time.time() period = end - start testCases.print(numTimeSteps, v1, v2, vJam, period) # plt.plot(numStepsList, treeVector) if 1 == 0: print("RT") printTree(model._rt, 5) print("BOND") printTree(model._bondValues, 5) print("OPTION") printTree(model._optionValues, 5)
print("ADD WORKDAYS") print(dt1, dt1.addWorkDays(2)) # The weekend has now been skipped # To add a month do print("ADD MONTHS") print(dt1, dt1.addMonths(2)) # An invalid date will throw an error # dt5 = FinDate(2019, 1, 31) # print(dt5) # You can use tenors - a number and a 'd', 'm' or 'y' in upper or lower case print("TENORS") print(dt1.addTenor("1d")) print(dt1.addTenor("2D")) print(dt1.addTenor("3M")) print(dt1.addTenor("4m")) print(dt1.addTenor("5Y")) print(dt1.addTenor("6y")) # You can subtract dates print("SUBTRACT DATES") dt6 = dt1.addTenor("5Y") dt7 = dt1.addTenor("10Y") dd = dt7 - dt6 print(dt6, dt7, dd) # check if a date is on a weekend print("WEEKEND TEST")
def test_FinBondOption(): settlementDate = FinDate(1, 12, 2019) issueDate = FinDate(1, 12, 2018) maturityDate = settlementDate.addTenor("10Y") coupon = 0.05 freqType = FinFrequencyTypes.SEMI_ANNUAL accrualType = FinDayCountTypes.ACT_ACT_ICMA bond = FinBond(issueDate, maturityDate, coupon, freqType, accrualType) tmat = (maturityDate - settlementDate) / gDaysInYear times = np.linspace(0, tmat, 20) dates = settlementDate.addYears(times) dfs = np.exp(-0.05 * times) discountCurve = FinDiscountCurve(settlementDate, dates, dfs) expiryDate = settlementDate.addTenor("18m") strikePrice = 105.0 face = 100.0 ########################################################################### strikes = [80, 90, 100, 110, 120] optionType = FinOptionTypes.EUROPEAN_CALL testCases.header("LABEL", "VALUE") price = bond.fullPriceFromDiscountCurve(settlementDate, discountCurve) testCases.print("Fixed Income Price:", price) numTimeSteps = 100 testCases.header("OPTION TYPE AND MODEL", "STRIKE", "VALUE") for strikePrice in strikes: sigma = 0.20 bondOption = FinBondOption(bond, expiryDate, strikePrice, face, optionType) model = FinModelRatesBDT(sigma, numTimeSteps) v = bondOption.value(settlementDate, discountCurve, model) testCases.print("EUROPEAN CALL - BK", strikePrice, v) for strikePrice in strikes: sigma = 0.20 bondOption = FinBondOption(bond, expiryDate, strikePrice, face, optionType) model = FinModelRatesBDT(sigma, numTimeSteps) v = bondOption.value(settlementDate, discountCurve, model) testCases.print("EUROPEAN CALL - BK", strikePrice, v) ########################################################################### optionType = FinOptionTypes.AMERICAN_CALL price = bond.fullPriceFromDiscountCurve(settlementDate, discountCurve) testCases.header("LABEL", "VALUE") testCases.print("Fixed Income Price:", price) testCases.header("OPTION TYPE AND MODEL", "STRIKE", "VALUE") for strikePrice in strikes: sigma = 0.20 bondOption = FinBondOption(bond, expiryDate, strikePrice, face, optionType) model = FinModelRatesBDT(sigma, numTimeSteps) v = bondOption.value(settlementDate, discountCurve, model) testCases.print("AMERICAN CALL - BK", strikePrice, v) for strikePrice in strikes: sigma = 0.20 bondOption = FinBondOption(bond, expiryDate, strikePrice, face, optionType) model = FinModelRatesBDT(sigma, numTimeSteps) v = bondOption.value(settlementDate, discountCurve, model) testCases.print("AMERICAN CALL - BK", strikePrice, v) ########################################################################### optionType = FinOptionTypes.EUROPEAN_PUT price = bond.fullPriceFromDiscountCurve(settlementDate, discountCurve) for strikePrice in strikes: sigma = 0.01 bondOption = FinBondOption(bond, expiryDate, strikePrice, face, optionType) model = FinModelRatesBDT(sigma, numTimeSteps) v = bondOption.value(settlementDate, discountCurve, model) testCases.print("EUROPEAN PUT - BK", strikePrice, v) for strikePrice in strikes: sigma = 0.20 bondOption = FinBondOption(bond, expiryDate, strikePrice, face, optionType) model = FinModelRatesBDT(sigma, numTimeSteps) v = bondOption.value(settlementDate, discountCurve, model) testCases.print("EUROPEAN PUT - BK", strikePrice, v) ########################################################################### optionType = FinOptionTypes.AMERICAN_PUT price = bond.fullPriceFromDiscountCurve(settlementDate, discountCurve) for strikePrice in strikes: sigma = 0.02 bondOption = FinBondOption(bond, expiryDate, strikePrice, face, optionType) model = FinModelRatesBDT(sigma, numTimeSteps) v = bondOption.value(settlementDate, discountCurve, model) testCases.print("AMERICAN PUT - BK", strikePrice, v) for strikePrice in strikes: sigma = 0.20 bondOption = FinBondOption(bond, expiryDate, strikePrice, face, optionType) model = FinModelRatesBDT(sigma, numTimeSteps) v = bondOption.value(settlementDate, discountCurve, model) testCases.print("AMERICAN PUT - BK", strikePrice, v)
def test_HullWhiteExampleTwo(): # HULL BOOK ZERO COUPON BOND EXAMPLE 28.1 SEE TABLE 28.3 # Replication may not be exact as I am using dates rather than times zeroDays = [ 0, 3, 31, 62, 94, 185, 367, 731, 1096, 1461, 1826, 2194, 2558, 2922, 3287, 3653 ] zeroRates = [ 5.0, 5.01772, 4.98282, 4.97234, 4.96157, 4.99058, 5.09389, 5.79733, 6.30595, 6.73464, 6.94816, 7.08807, 7.27527, 7.30852, 7.39790, 7.49015 ] times = np.array(zeroDays) / 365.0 zeros = np.array(zeroRates) / 100.0 dfs = np.exp(-zeros * times) startDate = FinDate(1, 12, 2019) sigma = 0.01 a = 0.1 strike = 63.0 face = 100.0 expiryDate = startDate.addTenor("3Y") maturityDate = startDate.addTenor("9Y") texp = (expiryDate - startDate) / gDaysInYear tmat = (maturityDate - startDate) / gDaysInYear numTimeSteps = None model = FinModelRatesHW(sigma, a, numTimeSteps) vAnal = model.optionOnZCB(texp, tmat, strike, face, times, dfs) # Test convergence numStepsList = range(100, 500, 50) analVector = [] treeVector = [] testCases.banner("Comparing option on zero coupon bond analytical vs Tree") testCases.header("NUMTIMESTEP", "VTREE_CALL", "VTREE_PUT", "VANAL CALL", "VANAL_PUT", "CALLDIFF", "PUTDIFF", "PERIOD") for numTimeSteps in numStepsList: start = time.time() model = FinModelRatesHW(sigma, a, numTimeSteps) model.buildTree(texp, times, dfs) vTree1 = model.optionOnZeroCouponBond_Tree(texp, tmat, strike, face) model = FinModelRatesHW(sigma, a, numTimeSteps + 1) model.buildTree(texp, times, dfs) vTree2 = model.optionOnZeroCouponBond_Tree(texp, tmat, strike, face) end = time.time() period = end - start treeVector.append(vTree1['put']) analVector.append(vAnal['put']) vTreeCall = (vTree1['call'] + vTree2['call']) / 2.0 vTreePut = (vTree1['put'] + vTree2['put']) / 2.0 diffC = vTreeCall - vAnal['call'] diffP = vTreePut - vAnal['put'] testCases.print(numTimeSteps, vTreeCall, vAnal['call'], vTreePut, vAnal['put'], diffC, diffP, period)
def test_BDTExampleTwo(): # Valuation of a European option on a coupon bearing bond # This follows example in Fig 28.11 of John Hull's book (6th Edition) # but does not have the exact same dt so there are some differences testCases.banner("===================== FIG 28.11 HULL BOOK =============") settlementDate = FinDate(1, 12, 2019) issueDate = FinDate(1, 12, 2015) expiryDate = settlementDate.addTenor("18m") maturityDate = settlementDate.addTenor("10Y") coupon = 0.05 freqType = FinFrequencyTypes.SEMI_ANNUAL accrualType = FinDayCountTypes.ACT_ACT_ICMA bond = FinBond(issueDate, maturityDate, coupon, freqType, accrualType) couponTimes = [] couponFlows = [] cpn = bond._coupon / bond._frequency numFlows = len(bond._flowDates) for i in range(1, numFlows): pcd = bond._flowDates[i - 1] ncd = bond._flowDates[i] if pcd < settlementDate and ncd > settlementDate: flowTime = (pcd - settlementDate) / gDaysInYear couponTimes.append(flowTime) couponFlows.append(cpn) for flowDate in bond._flowDates: if flowDate > settlementDate: flowTime = (flowDate - settlementDate) / gDaysInYear couponTimes.append(flowTime) couponFlows.append(cpn) couponTimes = np.array(couponTimes) couponFlows = np.array(couponFlows) strikePrice = 105.0 face = 100.0 tmat = (maturityDate - settlementDate) / gDaysInYear texp = (expiryDate - settlementDate) / gDaysInYear times = np.linspace(0, tmat, 11) dates = settlementDate.addYears(times) dfs = np.exp(-0.05 * times) testCases.header("LABEL", "VALUES") testCases.print("TIMES:", times) curve = FinDiscountCurve(settlementDate, dates, dfs) price = bond.cleanPriceFromDiscountCurve(settlementDate, curve) testCases.print("Fixed Income Price:", price) sigma = 0.20 # Test convergence numStepsList = [5] #[100, 200, 300, 400, 500, 600, 700, 800, 900, 1000] exerciseType = FinExerciseTypes.AMERICAN testCases.header("Values") treeVector = [] for numTimeSteps in numStepsList: model = FinModelRatesBDT(sigma, numTimeSteps) model.buildTree(tmat, times, dfs) v = model.bondOption(texp, strikePrice, face, couponTimes, couponFlows, exerciseType) testCases.print(v) treeVector.append(v['call']) if PLOT_GRAPHS: plt.plot(numStepsList, treeVector) # The value in Hull converges to 0.699 with 100 time steps while I get 0.70 if 1 == 0: print("RT") printTree(model._rt, 5) print("Q") printTree(model._Q, 5)
def test_FinBondOptionAmericanConvergenceTWO(): # Build discount curve settlementDate = FinDate(1, 12, 2019) discountCurve = FinDiscountCurveFlat(settlementDate, 0.05) # Bond details issueDate = FinDate(1, 12, 2015) maturityDate = settlementDate.addTenor("10Y") coupon = 0.05 frequencyType = FinFrequencyTypes.SEMI_ANNUAL accrualType = FinDayCountTypes.ACT_ACT_ICMA bond = FinBond(issueDate, maturityDate, coupon, frequencyType, accrualType) expiryDate = settlementDate.addTenor("18m") face = 100.0 spotValue = bond.cleanPriceFromDiscountCurve(settlementDate, discountCurve) testCases.header("LABEL", "VALUE") testCases.print("BOND PRICE", spotValue) testCases.header("PERIOD", "N", "EUR_CALL", "AMER_CALL", "EUR_PUT", "AMER_PUT") sigma = 0.01 a = 0.1 hwModel = FinModelRatesHW(sigma, a) K = 102.0 vec_ec = [] vec_ac = [] vec_ep = [] vec_ap = [] numStepsVector = range(10, 500, 10) for numSteps in numStepsVector: hwModel = FinModelRatesHW(sigma, a, numSteps) start = time.time() europeanCallBondOption = FinBondOption(bond, expiryDate, K, face, FinOptionTypes.EUROPEAN_CALL) v_ec = europeanCallBondOption.value(settlementDate, discountCurve, hwModel) americanCallBondOption = FinBondOption(bond, expiryDate, K, face, FinOptionTypes.AMERICAN_CALL) v_ac = americanCallBondOption.value(settlementDate, discountCurve, hwModel) europeanPutBondOption = FinBondOption(bond, expiryDate, K, face, FinOptionTypes.EUROPEAN_PUT) v_ep = europeanPutBondOption.value(settlementDate, discountCurve, hwModel) americanPutBondOption = FinBondOption(bond, expiryDate, K, face, FinOptionTypes.AMERICAN_PUT) v_ap = americanPutBondOption.value(settlementDate, discountCurve, hwModel) end = time.time() period = end - start testCases.print(period, numSteps, v_ec, v_ac, v_ep, v_ap) vec_ec.append(v_ec) vec_ac.append(v_ac) vec_ep.append(v_ep) vec_ap.append(v_ap) if plotGraphs: plt.figure() plt.plot(numStepsVector, vec_ac, label="American Call") plt.legend() plt.figure() plt.plot(numStepsVector, vec_ap, label="American Put") plt.legend()